Manchester United legend Beckham, along with the fellow owners of the newly-formed Inter Miami, are on the hunt for their first boss.
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And according to the Daily Mirror, Moyes is on a shortlist of managers the club are considering for the position.
Thierry Henry and Carlo Ancelotti are also believed to be in the running for the job.
Moyes, 55, has been out of work since his short-term spell at West Ham came to an end in May 2018.
But that extended break out of the game could come to an end sooner rather than later for the former United boss, with Inter Miami entering the MLS in February.
The club have already sold 8,000 season tickets as they get ready to battle with the best America has to offer.